Presbyopia lens with pupil size correction based on level of refractive error

ABSTRACT

Ophthalmic lenses for the treatment of presbyopia may be improved to enhance the visual experience of the patient. By adjusting the optical design of presbyopic lenses to account for changes in pupil size due to the degree of myopia or hyperopia, an enhanced visual experience may be achieved independent of the level of ametropia.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to contact lenses for correctingpresbyopia, and more particularly to contact lenses for correctingpresbyopia that are scaled based upon pupil size as it relates torefractive error to ensure that the design provides the same visualexperience independent of the level of ametropia or refractive error.The present invention also relates to a method for adjusting the opticaldesigns for lenses for correcting presbyopia to account for changes inpupil size as it relates to ametropia.

2. Discussion of the Related Art

As individuals age, their eyes are less able to accommodate, or bendtheir natural or crystalline lens, to focus on objects that arerelatively near to the observer. This condition is known as presbyopia.More specifically, when an individual is born, the crystalline lens ispliable which makes it capable of a high degree of accommodation. As theindividual ages, the crystalline lens gradually becomes more rigid andthus less able to accommodate. Similarly, for persons who have had theirnatural or crystalline lens removed and an intraocular lens or IOLinserted as a replacement, the ability to accommodate is absent.Although the intent of an accommodating IOL is to address this potentialshortcoming, current accommodating IOL designs and concepts arerelatively new and continue to evolve.

Various classes of contact lens and intra-ocular designs have beenoffered for the treatment of presbyopia. These include bi-focal andmulti-focal contact lenses of various forms, including concentric rings,aspheric designs, as well as diffractive designs. These designs aretypically depicted in the patent literature by their power profiles.Even if described by surface or other attributes, the power profile fora given design may be determined.

An example of a power profile for a concentric ring type design isillustrated in FIG. 1. The horizontal axis shows the radial positionfrom the center of the lens in millimeters. The vertical axis shows thecontact lens power, in diopters (D), relative to the label power of thecontact lens. This particular design consists of five concentric rings.The contact lens power plotted here is relative to the label power. Thelabel power is the power required to compensate for the level ofametropia or refractive error of the patient. For example, it may bedetermined by an eye care professional that an individual with myopia ornearsightedness requires −2.75 D lens to correct their ametropia. Thelabel power of the contact lens selected will be −2.75 D.

For a particular design, such as the one illustrated in FIG. 1, there isrequired a set of lenses of a range of label powers. Typically aparticular design such as the one illustrated in FIG. 1 is provided withlabel powers from −12.00 D to 8.00 D in 0.25 D increments. The prior-art(patent or otherwise) typically describes an optical design intended forthe treatment of presbyopia for a single label power. The method fordetermining the designs at other label powers is not specified butimplied in the description of the design at the nominal power. Theimplied method for the design from FIG. 1 to create the set of designsto cover a range of label powers is to take the nominal design and addto it a constant power equal to the label power. The set of powerprofiles for this design in 1.0 D increments from −8.0 D to +6.0 D labelpowers is illustrated in FIG. 2.

There are many forms of bi-focal or multi-focal contact lenses for thecorrection of presbyopia. These design forms include concentric rings,aspheric designs, as well as diffractive designs. All of these designsfunction by providing a range of powers within the pupil of the eye. Forexample, a concentric ring design may have a central ring that providespowers that are nominally equal to the power required to correct thedistance vision of the subject, an adjacent ring that provides nearpowers, and an outer ring that also provides distance powers. There mayalso be versions or variations with intermediate powers to addresssituations between near and far distances, for example, computer screenviewing. An aspheric design may be considered a multi-focal orprogressive type design that provide powers for a given pupil size thatgradually change from being plus to distance in the center of the lensand providing powers for near vision correction to having distancepowers at the edge of the pupil to provide distance vision correction.

Pupil size depends upon a number of factors, including light level. Muchof the design work and prior art for presbyopic designs is concernedwith optimizing the design performance for a range of light levels andthus pupil sizes. In designing these lenses for presbyopes, the pupilsize is taken into account. The approach to doing this depends upon theintent of the design. One goal may be to make a design independent ofpupil size so that vision will stay constant as light levels change andpupil sizes change. Alternatively, the intent may be to provide a lensthat gives preference to near vision for small pupils and distancevision for large pupils such as is done by many of the center neardesigns. Or, the intent may be to provide a lens that gives preferenceto distance vision for small pupils and near vision for large pupilssuch as is done by many of the center distance designs. The designpossibilities and permutations are essentially endless.

Pupil size also depends upon the level of ametropia. Referring now toFIGS. 3, 4 and 5, there is illustrated in graphical format therelationship between pupil size and refractive error for a givenluminance level. More specifically, FIGS. 3-5 illustrated pupil sizedata collected at 2.5, 50, and 250 cd/m² (candela per square meter)luminance levels. This data is for subjects greater than forty (40)years old representing the presbyopic population. The pupil size data onthe vertical axis is plotted against the refractive error in Diopters onthe horizontal axis. As may be seen from the figures, the pupil sizes atall light levels are smaller for hyperopes than for myopes. Accordingly,since the pupil size at a given light level varies with the refractiveerror, then lenses for the treatment of presbyopia are needed that havetheir designs scaled based upon pupil size to ensure that the designsperform consistently independent of the refractive error beingcorrected.

SUMMARY OF THE INVENTION

The contact lenses and the design methods therefor of the presentinvention overcome the disadvantages associated with the prior art asbriefly described above.

In accordance with one aspect, the present invention is directed to amethod for improving ophthalmic lenses for the treatment of presbyopia.The method comprises the steps of creating a base optical design withpredetermined features for a lens for treating presbyopia, determiningthe power profile of the base optical design, P_(nominal), and scalingthe radial location of the predetermined features within the baseoptical design in proportion to the population average pupil size forthe degree of ametropia of a target individual.

In accordance with another aspect, the present invention is directed toa method for improving ophthalmic lenses for the treatment ofpresbyopia. The method comprises the steps of creating a base opticaldesign with predetermined features for a lens for treating presbyopia,determining the power profile of the base optical design, P_(nominal),and scaling the radial location of the predetermined features within thebase optical design in proportion to a measured pupil size of anindividual.

In accordance with yet another aspect, the present invention is directedto a method for improving ophthalmic lenses for the treatment ofpresbyopia. The method comprises the steps of creating a base opticaldesign with predetermined features for a lens for treating presbyopia,determining the power profile of the base optical design at a nominalprescription power, creating a visual merit function for optimization,and minimizing the difference between the visual merit function at thenominal prescription power and the visual merit function at theprescription powers other than at the nominal prescription power.

In accordance with still yet another aspect, the present invention isdirected to a set of lenses for treating presbyopia over a range ofdegrees of ametropia. The set of lenses being designed by creating abase optical design with predetermined features for a lens for treatingpresbyopia, determining the power profile of the base optical design,P_(nominal), and scaling the radial location of the predeterminedfeatures within the base optical design in proportion to the populationaverage pupil size for the degree of ametropia of a target individual.

In accordance with another aspect, the present invention is directed toa set of lenses for treating presbyopia over a range of degrees ofametropia. The set of lenses being designed by creating a base opticaldesign with predetermined features for a lens for treating presbyopia,determining the power profile of the base optical design, P_(nominal),and scaling the radial location of the predetermined features within thebase optical design in proportion to a measured pupil size of anindividual.

In accordance with yet another aspect, the present invention is directedto a set of lenses for treating presbyopia over a range of degrees ofametropia. The set of lenses being designed by creating a base opticaldesign with predetermined features for a lens for treating presbyopia,determining the power profile of the base optical design at a nominalprescription power, creating a visual merit function for optimization,and minimizing the difference between the visual merit function at thenominal prescription power and the visual merit function at theprescription powers other than at the nominal prescription power.

In accordance with still another aspect, the present invention isdirected to a set of lenses for treating presbyopia over a range ofdegrees of ametropia. The set of lenses being designed with a powerprofile given by

P _(Rx)(r)=P ₂(M ₁ *r+M ₂ *r ²+ . . . )−SA _(eye) *r ²,

where P₂ is given by

P ₂(r)=P ₁ +Rx,

and

P1(r)=P _(nominal)(r)−Rx _(nominal) +SA _(eye) *r ²,

where SA_(eye) is the spherical aberration, r is the radial distancefrom the center of the lens, and P_(nominal)(r) is the power profile forthe nominal design for the correction of an eye with a sphericalrefractive need of Rx_(nominal) diopters.

The present invention is directed to lenses, for example, contact lensesand intraocular lenses, for the treatment of presbyopia that are scaledbased upon pupil size data to ensure that the design provides the samevisual experience independent of the level of ametropia of the patient.The present invention is also directed to methods for adjusting theoptical designs for presbyopic lenses to account for changes in pupilsize to ensure that the design gives the same visual experienceindependent of the level of ametropia of the patient. More specifically,the present invention provides a means for adjusting multi-focal andbi-focal designs such that the designs will perform consistently acrossthe population, independent of the degree of ametropia. The opticaldesigns of the lenses for presbyopia described herein are unique foreach spherical prescription (Rx) to take into account the fact that thesize of the pupil changes with the level or degree of ametropia. Theresulting lenses may then be a low and high add, or a low, medium andhigh add combination, the designs of which may vary by prescription.

While the pupil size data demonstrates that pupil sizes on average aresmaller for individuals with hyperopia than for individuals with myopiaat and across all light levels, it also shows that there is greatvariability among subjects for a given level of ametropia. The method ofthe present invention may also be utilized to scale a design forpresbyopia that is constructed and optimized for a particular set ofpupil sizes at low, medium and brighter light conditions to be used onan individual that has either a smaller or a larger set of pupil sizesfor a given light level. In this case, either the designs are customizedfor an individual or there may be alternate sets of designs where one ofthe fit criteria utilized by eye care professionals is patient pupilsize, thus providing patients with an improved visual experience.

The first method in accordance with the present invention provides ameans to analytically scale a power profile for a design at oneprescription to the full range of required prescriptions to providesimilar visual performance across the full range of ametropia.

The second method in accordance with the present invention provides ameans to scale a power profile for a design at one prescription to thefull range of required prescriptions to provide similar visualperformance across the full range of ametropia using an optimizationmethod that uses as the merit function a metric that ensures that thevisual performance experienced by the wearers depends as little aspossible on the level of ametropia.

The overall methodology of the present invention provides a means formodifying existing contact lenses. The methodology allows for creatingcontact lenses for treating presbyopia with improved visual acuity and abetter visual experience for the user.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages of the invention will beapparent from the following, more particular description of preferredembodiments of the invention, as illustrated in the accompanyingdrawings.

FIG. 1 is a graphical representation of the power profile of anexemplary concentric ring contact lens.

FIG. 2 is a graphical representation of a set of power profiles of anexemplary concentric ring contact lens at different prescriptionstrengths.

FIG. 3 is a graphical representation of pupil size versus refractiveerror data at a 2.5 cd/m² luminance level.

FIG. 4 is a graphical representation of pupil size versus refractiveerror data at a 50 cd/m² luminance level.

FIG. 5 is a graphical representation of pupil size versus refractiveerror data at a 250 cd/m² luminance level.

FIG. 6 is a graphical representation of three fits of the data of FIGS.3, 4 and 5.

FIG. 7 is a graphical representation of magnification factor as afunction of Rx.

FIG. 8 is a graphical representation of a family of power profiles.

FIG. 9 is a series of graphical representations of predicted logmaracuity versus vergence for three different design methods on aconcentric ring lens.

FIGS. 10-12 are simplified replots of the data illustrated in FIG. 9.

FIG. 13 is a graphical representation of a series of power profilesversus radial position from lens center generated utilizing a scalingmethod on a concentric ring lens in accordance with the presentinvention.

FIG. 14 is a graphical representation of a series of power profilesversus radial position from lens center generated utilizing anoptimization method on a concentric ring lens in accordance with thepresent invention.

FIG. 15 is a graphical representation of the power profile of anexemplary progressive multi-focal contact lens.

FIG. 16 is a graphical representation of a series of power profilesversus radial position from lens center generated utilizing a scalingmethod on a progressive multi-focal lens in accordance with the presentinvention.

FIG. 17 is a graphical representation of a series of power profilesversus radial position from lens center generated utilizing a scalingmethod on a progressive multi-focal lens with the Rx subtracted fromeach in accordance with the present invention.

FIG. 18 is a graphical representation of a series of power profilesversus radial position from lens center generated utilizing anoptimization method on a progressive multi-focal lens in accordance withthe present invention.

FIG. 19 is a series of graphical representations of predicted longmaracuity versus vergence for three different design methods on aprogressive multi-focal lens.

FIGS. 20-22 are simplified replots of the data illustrated in FIG. 19.

FIG. 23 is a graphical representation of magnification factor as afunction of radial position for different Rx values.

FIG. 24 is a graphical representation of power profiles for a family oflenses created utilizing a scaling method with the magnification factorM altered as shown in FIG. 23.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention is directed to methods for adjusting the opticaldesigns for lenses for the correction of presbyopia to account forchanges in pupil size to ensure that the design gives the same visualexperience independent of the level of ametropia of the patient and theresultant lenses. In accordance with one exemplary embodiment, themethod provides a means to analytically scale a power profile for adesign at one prescription to the full range of required prescriptionsto provide similar visual performance across the full range ofametropia. This is the analytical scaling method. In accordance withanother exemplary embodiment, the method provides a means to scale apower profile for a design at one prescription to the full range ofrequired prescriptions to provide similar visual performance across thefull range of ametropia using an optimization method that utilizes asthe merit function or metric that ensures that the visual performanceexperienced by the users depends as little as possible on the level ofametropia. This is the optimization method. As stated above, the methodsmay be utilized in any suitable lens, and in the exemplary embodimentsdescribed below, a concentric ring design and a progressive multi-faceddesign are set forth. The processes describe herein utilize the datathat indicate pupil sizes for hyperopes and myopes are different as isexplained in detail herein.

The present invention may be utilized in a number of ophthalmic lenses,for example, intraocular lenses and contact lenses. For ease ofexplanation; however, the present invention is described with respect tocontact lenses. Contact lenses or contacts are simply lenses placed onthe eye. Contact lenses are considered medical devices and may be wornto correct vision and/or for cosmetic or other therapeutic reasons.Contact lenses have been utilized commercially to improve vision sincethe 1950s. Early contact lenses were made or fabricated from hardmaterials, were relatively expensive and fragile. In addition, theseearly contact lenses were fabricated from materials that did not allowsufficient oxygen transmission through the contact lens to theconjunctiva and cornea which potentially could cause a number of adverseclinical effects. Although these contact lenses are still utilized, theyare not suitable for all patients due to their poor initial comfort.Later developments in the field gave rise to soft contact lenses, basedupon hydrogels, which are extremely popular and widely utilized today.Specifically, silicone hydrogel contact lenses that are available todaycombine the benefit of silicone, which has extremely high oxygenpermeability, with the proven comfort and clinical performance ofhydrogels. Essentially, these silicone hydrogel based contact lenseshave higher oxygen permeabilities and are generally more comfortable towear than the contact lenses made of the earlier hard materials.However, these new contact lenses are not totally without limitations.

Currently available contact lenses remain a cost effective means forvision correction. The thin plastic lenses fit over the cornea of theeye to correct vision defects, including myopia or nearsightedness,hyperopia or farsightedness, astigmatism, i.e. asphericity in thecornea, and presbyopia i.e. the loss of the ability of the crystallinelens to accommodate. Contact lenses are available in a variety of formsand are made of a variety of materials to provide differentfunctionality. Daily wear soft contact lenses are typically made fromsoft polymer-plastic materials combined with water for oxygenpermeability. Daily wear soft contact lenses may be daily disposable orextended wear disposable. Daily disposable contact lenses are usuallyworn for a single day and then thrown away, while extended weardisposable contact lenses are usually worn for a period of up to thirtydays. Colored soft contact lenses use different materials to providedifferent functionality. For example, a visibility tint contact lensuses a light tint to aid the wearer in locating a dropped contact lens,enhancement tint contact lenses have a translucent tint that is meant toenhance one's natural eye color, the color tint contact lens comprises adarker, opaque tint meant to change one's eye color, and the lightfiltering tint contact lens functions to enhance certain colors whilemuting others. Rigid gas permeable hard contact lenses are made fromsilicone polymers but are more rigid than soft contact lenses and thushold their shape and are more durable. Bifocal contact lenses aredesigned specifically for patients with presbyopia and are available inboth soft and rigid varieties. Toric contact lenses are designedspecifically for patients with astigmatism and are also available inboth soft and rigid varieties. Combination lenses combining differentaspects of the above are also available, for example, hybrid contactlenses.

For purposes of the present invention a contact lens is defined by atleast two distinct regions. The inner region or optical zone from whichthe vision correction is obtained and the outer peripheral zone of thecontact lens that provides mechanical stability of the contact lens oneye. In some cases or contact lens designs an intermediate zone orregion located between the inner optical zone and the outer peripheralzone may be used for blending the two aforementioned zones in a smoothmanner such that discontinuities do not occur. A contact lens is alsodefined by a front surface or surface power, a back curve or base curveand an edge.

The inner region or optical zone provides vision correction and isdesigned for a specific need such as single vision myopia or hyperopiacorrection, astigmatism vision correction, bi-focal vision correction,multi-focal vision correction, custom correction or any other designthat may provide vision correction. In other words, the optical zonecomprises the visual power correction for the wearer's ametropia andpresbyopia. Ametropia is defined as the optical power needed to providegood visual acuity, generally at far distance. It is recognized thatthis would include myopia or hyperopia, and astigmatism concurrent witheither. Presbyopia is corrected by adding algebraically plus opticalpower to a portion of the optical zone to correct the wearer's nearvisual acuity requirements. It is recognized that these optical powersmay be created by refractive means, diffractive means, or both. Theouter periphery or peripheral zone provides stabilization of the contactlens on the eye including centration and orientation.

Orientation and stabilization is fundamental when the optical zoneincludes non-rotationally symmetric features, such as astigmaticcorrection and/or high order aberrations correction. The intermediateregion or zone ensures that the optical zone and the peripheral zone areblended with tangent curves. It is important to note that both theoptical zone and the peripheral zone may be designed independently,though sometimes their designs are strongly related when particularrequirements are necessary. For example, the design of a toric lens withan astigmatic optical zone might require a particular peripheral zonefor maintaining the contact lens at a predetermined orientation on theeye.

Toric contact lenses have different designs than spherical contactlenses. The optical zone portions of toric contact lenses have twopowers in them, spherical and cylindrical, created with curvaturesgenerally at right angles to each other. The powers are required tomaintain position at the specific angle, cylinder axis, on the eye toprovide the required astigmatic vision correction. The mechanical orouter peripheral zone of toric contact lenses typically comprises astabilization means to properly rotate and orient the cylindrical orastigmatic axis into position while being worn on the eye. Rotating thecontact lens to its proper position when the contact lens moves, or whenthe contact lens is inserted is important in producing a toric contactlens.

The first step in creating lenses in accordance with the presentinvention is creating an optical design for a bi-focal or multi-focalcontact lens. The design types or methods for creating this design arenot fixed by or defined by the present invention. Therefore, the designtype may be any number of types, including concentric ring designs,designs with continuous power profiles and aspheric surfaces, designsthat use diffractive surfaces, and the like. In other words, anysuitable lens may be utilized.

The next step in the process is determining the power profile of thedesign. The power profile, as illustrated in FIG. 1 for an exemplaryconcentric ring design, is power in diopters calculated as thereciprocal of the distance from the lens in meters to the focal pointfor light from a given radial position in the pupil. The powerP_(nominal)(r) for the nominal design is a function of the radialposition r. This lens is designed for an eye with a spherical refractiveneed, i.e. the spherical prescription, or Rx_(nommal). The notation usedhere and throughout this description assumes that the power profile isradially symmetric, but this is not a limitation of the presentinvention. More generally, there is also a polar angle dependence of thepower profile.

From the pupil size data provided and described in the figures andspecification, it is known that the pupil sizes for hyperopes aresmaller than for myopes for equivalent light levels. The central idea ofthe present invention is to scale the radial location of features withina given design that impact the presbyopic performance so that thelocation of the features are always located at a constant locationrelative to the pupil for a given light level. Since the pupil size fora given light level changes in proportion to the degree of ametropia,then it follows that the radial position of the design features mustpreferably likewise change in proportion to the degree of ametropia.

Starting with the power profile P_(nommal)(r) for the nominal design forthe correction of an eye with a spherical refractive need ofRx_(nominal) diopters the power profile P₁(r) is given by

P ₁(r)=P _(nominal)(r)−Rx _(nominal) SA _(eye) *r ²,  (1)

where SA_(eye) is the spherical aberration and r is the radial distancefrom the center of the lens. The power profile P₁(r) is the powerprofile for the lens plus eye combination for the nominal design placedon an eye with nominal refractive need assuming that the eye has aspherical aberration SA_(ye). The spherical aberration is in units ofdiopters/mm² and has values typically from 0 to 0.1 D/mm².

The power profile, P₁(r), is next shifted by the power required to makethe design suitable for an eye with a refractive need of Rx diopters.This power, P₂(r), is simply given by

P ₂(r)=P ₁(r)+Rx.  (2)

Substituting for P₁(r) from equation (1) into equation (2) results in

P ₂(r)=P _(nominal)(r)+SA _(eye) *r ² +Rx−Rx _(nommal).  (3)

From pupil size data at constant light levels from subjects representingthe full range of possible refractive errors one may determine themagnification factor, M, that is applied to the power profile P₂ todetermine the scaled power profile for the design at a differentprescription or Rx. The scaled power P_(Rx)(r) is given by

P _(Rx)(r)=P ₂(M*r)−SA _(eye) *r ².  (4)

In accordance with the present invention, the magnification factor M maybe approximated by a linear function. The value of M at a given Rx fallswithin the range of values given by

M(Rx)=m·(Rx−Rx _(nominal))+1  (5)

where m varies according to 0.008<m<0.012.

To better understand this, refer first to the data illustrated in FIGS.3-5. This data is for subjects greater than forty (40) years oldrepresenting the presbyopic population. The pupil diameters weredetermined for luminance levels of 2.5 cd/m², 50 cd/m², and 250 cd/m².These three fits to the data are plotted together in FIG. 6 as set forthin detail subsequently.

The magnification factor, M, is determined from the pupil data as shownin the following examples. In a first example, the lens is a concentricring type multi-focal lens. The power profile P_(nominal)(r) atRx_(nominal)=0.0 D is illustrated in FIG. 1. The pupil radius at threedistinct luminance levels is summarized by the plot illustrated in FIG.6. Referring to FIG. 6, at Rx_(nominal)=0 the radius values r01, r02,and r03 for each of the luminance values tested (250 cd/m², 50 cd/m²,and 2.5 cd/m²), in addition to the zero value r00 are determined. Thesevalues may be represented by the vector {right arrow over (r)}₀ given by

{right arrow over (r)} ₀ =[r ₀₀ r ₀₁ r ₀₂ r ₀₀₃].  (6)

Likewise, the vector {right arrow over (r)}₁ is determined from thevalues at the Rx of the target design. In FIG. 6, the target Rx is 6.0D, and the vector {right arrow over (r)}₁ is given by

{right arrow over (r)} ₀ =[r ₁₀ r ₁₁ r ₁₂ r ₁₃].  (7)

The magnification factor M relates {right arrow over (r)}₀ and {rightarrow over (r)}₁ as follows

{right arrow over (r)} ₀ =M·{right arrow over (r)} _(1.)  (8)

M is determined numerically, preferably by a least squares minimization.

Alternately, the factor relating {right arrow over (r)}₀ and {rightarrow over (r)}₁ may be a higher order function such as a quadratic orcubic function to provide a better fit to the pupil data. In this caseequation (4) may become

P _(Rx)(r)=P ₂(M ₁ *r+M ₂ *r ²+ . . . )−SA _(eye) *r ².  (9)

FIG. 7 illustrates, for this example, the magnification factors as afunction of Rx. Note that M=1 at Rx_(nominal)=0, which is as expected.

Applying these magnification factors across a range of target Rx valuesfrom −8.0 D to +6.0 D in 1.0 D increments results in the family of powerprofiles illustrated in FIG. 8. For hyperopes, who have smaller pupilsizes, the features in the power profile are located more toward thecenter of the optics. For myopes, who have larger pupil sizes, thefeatures in the power profile are located more toward the periphery ofthe optic.

To further refine the mapping to alternate pupil sizes or as analternate to the calculations set forth above, an optimization proceduremay be implemented whereby the power profile at Rx values other thanRx_(nominal) are determined which minimize the difference between avisual performance metric at the alternate Rx's and the visualperformance metric at Rx_(nominal) U.S. Pat. No. 7,625,086 describes amethod for calculating a predicted logmar acuity (“VA”) for a contactlens and eye combination. This VA calculation may be used as a visualperformance metric for optimization, although other metrics such asmodulated transfer function (MTF) or root mean square (RMS) spot sizeare also possible. The preferred method for creating the merit functionis to calculate the through vergence (object distance from infinity to40 cm, or equivalently in diopters from 0 D to 2.5 D) at Rx_(nominal)for low, medium and high luminance levels and define the merit functionas the difference between those VA values and the values at the new Rx(which has different pupil sizes at the designated luminance levels).The power profile of the design is then optimized in a least squaressense to minimize the difference in the through vergence VA between thedesigns and Rx and Rx_(nominal).

FIG. 9 graphically illustrates, for a concentric ring zone design lens(example 1) a comparison between prior art lenses, lenses made via thescaling method and lenses made via the optimization method. The data isalso presented in Table 1 given below. FIG. 9 illustrates three rows andthree columns of through vergence calculations for designs from −9 D to+6 D (−9 D, −6 D, −3 D, 0 D, 3 D, and 6 D). In these designsRx_(nominal)=0. The first row is for luminance of 250 cd/m², the secondrow with 50 cd/m2 and the third row with 2.5 cd/m². The first columnillustrates the through vergence results with the power profiles scaledacross Rx using the method of the prior art. The middle columnillustrates the scaling method and the right column shows theoptimization method. On each plot is also shown the RMS value, which isthe RMS error between the target through vergence VA at Rx_(nominal) andthe actual value. As one can see, in a majority of the cases, thescaling method provides an improvement over the prior art and theoptimization method provides an even further improvement consistentlyresulting in lower RMS values for the three pupil sizes for all Rx's.

FIGS. 10-12 are graphical representations of the same data plotteddifferently and with fewer plots combined so that it is easier to seethe advantages of the exemplary methods of the present invention. FIG.10 is for 250 cd/m2, FIG. 11 is for 50 cd/m2 and FIG. 12 is for 5 cd/m2.

FIG. 14, like FIG. 8, illustrates the power profiles for the resultantdesigns using the scaling method. In this case, they are all normalizedto the same Rx (e.g. Rx=0). FIG. 13 illustrates the power profiles usingthe optimization method.

TABLE 1 Pupil Prior Scaled Optimized Rx = −9D EPD 2.8 0.032 0.014 0.014EPD 3.6 0.086 0.032 0.025 EPD 5.8 0.297 0.324 0.204 Rx = −6D EPD 2.70.017 0.009 0.009 EPD 3.5 0.055 0.021 0.016 EPD 5.7 0.243 0.226 0.131 Rx= −3D EPD 2.7 0.006 0.004 0.005 EPD 3.4 0.027 0.010 0.008 EPD 5.5 0.1570.104 0.068 Rx-0D EPD 2.6 0.000 0.000 0.000 EPD 3.3 0.000 0.000 0.000EPD 5.3 0.000 0.000 0.000 Rx = 3D EPD 2.5 0.005 0.005 0.005 EPD 3.20.025 0.010 0.008 EPD 5.1 0.152 0.131 0.061 Rx = 6D EPD 2.4 0.011 0.0090.009 EPD 3.1 0.048 0.019 0.015 EPD 4.9 0.234 0.237 0.124

In a second example, a progressive multi-focal lens design is utilizedto illustrate the results of the different methods. The nominal powerprofile for the progressive multi-focal lens design at Rx_(nominal)=0 isillustrated in FIG. 15. Applying the same magnification factor as in theprevious example, the resulting designs using the scaling method areillustrated in FIG. 16. Because it is difficult to observe in FIG. 16the scaling of the presbyopic features in the design, the same designsare replotted in FIG. 17 with the Rx subtracted from each. The resultsusing the optimization method are illustrated in FIG. 18. The throughfocus VA results comparing the prior art, the scaling method, and theoptimization method are illustrated in FIGS. 19-22. The RMS valuesshowing the difference in through focus VA (via model) between thetarget values and the design values are summarized in Table 2.

TABLE 2 Pupil Prior Scaled Optimized Rx = −9D EPD 2.8 0.017 0.018 0.016EPD 3.6 0.036 0.029 0.025 EPD 5.8 0.401 0.336 0.349 Rx = −6D EPD 2.70.011 0.012 0.009 EPD 3.5 0.023 0.018 0.017 EPD 5.7 0.298 0.256 0.200 Rx= −3D EPD 2.7 0.005 0.006 0.005 EPD 3.4 0.011 0.008 0.008 EPD 5.5 0.1450.135 0.104 Rx = 0D EPD 2.6 0.000 0.000 0.000 EPD 3.3 0.000 0.000 0.000EPD 5.3 0.000 0.000 0.000 Rx = 3D EPD 2.5 0.005 0.006 0.005 EPD 3.20.011 0.008 0.008 EPD 5.1 0.145 0.128 0.100 Rx = 6D EPD 2.4 0.009 0.0120.009 EPD 3.1 0.021 0.016 0.015 EPD 4.9 0.256 0.231 0.177

In accordance with another exemplary embodiment, the results of thesecond example may be refined. In this exemplary embodiment, themagnification factor M may be adjusted so that it is no longer constantwith radial position. Adjusting the magnification factor with lensradius is useful when it is desired at or near the periphery of the lensthat the design features be constant across SKUs. This could be forvision reasons, but more likely for mechanical considerations. FIG. 23illustrates the magnification factor M as a function of radial position.In the central portion of the aperture, the M is the same as in theprevious example. Beyond a radius of 2 mm the factor M is equal to one.There is an approximately 0.5 mm transition region. FIG. 24 shows thepower profiles for a family of designs created using the scaling methodwith the magnification factor M altered as shown in FIG. 23.

The present invention is for both a method of design and the resultinglens designs that provide an improved lens for presbyopes that isdesigned for a particular set of pupil sizes at low, medium, and brightluminance levels to be scaled and to be used on a subject with adifferent pupil size response to low, medium, and bright luminancelevels. In particular, it is known that pupil sizes change withametropia (as measured by sphere Rx) so therefore this method may beapplied to any design that is intended to be used on a generalpopulation where the design is done for the “average” eye. In this casethe “average” eye changes with Rx so the design is adjusted by Rx usingeither the scaling method or the optimization method to provide improvedperformance relative to the prior art.

Although shown and described in what is believed to be the mostpractical and preferred embodiments, it is apparent that departures fromspecific designs and methods described and shown will suggest themselvesto those skilled in the art and may be used without departing from thespirit and scope of the invention. The present invention is notrestricted to the particular constructions described and illustrated,but should be constructed to cohere with all modifications that may fallwithin the scope of the appended claims.

1. A method for improving ophthalmic lenses for the treatment ofpresbyopia, the method comprising the steps of: creating a base opticaldesign with predetermined features for a lens for treating presbyopia;determining the power profile of the base optical design, P_(nominal);and scaling the radial location of the predetermined features within thebase optical design in proportion to the population average pupil sizefor the degree of ametropia of a target individual.
 2. The method forimproving ophthalmic lenses for the treatment of presbyopia according toclaim 1, wherein the step of creating a base optical design comprisescreating a concentric ring design.
 3. The method for improvingophthalmic lenses for the treatment of presbyopia according to claim 1,wherein the step of creating a base optical design comprises creating acontinuous power profile design.
 4. The method for improving ophthalmiclenses for the treatment of presbyopia according to claim 1, wherein thestep of creating a base optical design comprises creating an asphericsurface design.
 5. The method for improving ophthalmic lenses for thetreatment of presbyopia according to claim 1, wherein the step ofscaling the radial location of the predetermined features within thebase optical design in proportion to the population average pupil sizefor the degree of ametropia of a target individual comprises:determining a magnification factor M that relates the pupil sizes at arange of luminance levels for the ametropia level of the base design tothe pupil sizes for the same luminance levels for the population averageat the targeted degree of ametropia; and scaling the power profile ofthe base design, P_(nominal), according to the following equations toobtain the power profile at the prescribed prescription, Rx, or degreeof ametropia,P ₂(r)=P _(nominal)(r)+SA _(eye) *r ² +Rx−Rx _(nominal), andP _(Rx)(r)=P ₂(M*r)−SA _(eye) *r ², wherein SA_(eye) is the sphericalaberration and r is the radial distance from the center of the lens. 6.The method for improving ophthalmic lenses for the treatment ofpresbyopia according to claim 1, wherein the step of scaling the radiallocation of the predetermined features within the base optical design inproportion to the population average pupil size for the degree ofametropia of a target individual comprises: determining magnificationfactor factors M₁ through M_(n) that relates the pupil sizes at a rangeof luminance levels for the ametropia level of the base design to thepupil sizes for the same luminance levels for the population average atthe targeted degree of ametropia; and scaling the power profile of thebase design, P_(nominal), according to the following equations to obtainthe power profile at the prescribed prescription, Rx, or degree ofametropia,P ₂(r)=P _(nominal)(r)+SA _(eye) *r ² +Rx−Rx _(nominal), andP _(Rx)(r)=P ₂(M ₁ *r+M ₂ *r ²+ . . . )−SA _(eye) *r ², wherein SA_(eye)is the spherical aberration and r is the radial distance from the centerof the lens.
 7. A method for improving ophthalmic lenses for thetreatment of presbyopia, the method comprising the steps of: creating abase optical design with predetermined features for a lens for treatingpresbyopia; determining the power profile of the base optical design,P_(nominal); and scaling the radial location of the predeterminedfeatures within the base optical design in proportion to a measuredpupil size of an individual.
 8. The method for improving ophthalmiclenses for the treatment of presbyopia according to claim 7, wherein thestep of creating a base optical design comprises creating a concentricring design.
 9. The method for improving ophthalmic lenses for thetreatment of presbyopia according to claim 7, wherein the step ofcreating a base optical design comprises creating a continuous powerprofile design.
 10. The method for improving ophthalmic lenses for thetreatment of presbyopia according to claim 7, wherein the step ofcreating a base optical design comprises creating an aspheric surfacedesign.
 11. The method for improving ophthalmic lenses for the treatmentof presbyopia according to claim 7, wherein the step of scaling theradial location of the predetermined features within the base opticaldesign in proportion to a measure pupil size of an individual comprises:determining a magnification factor M that relates the pupil sizes at arange of luminance levels for the ametropia level of the base design tothe measured pupil size for the same luminance of the individual; andscaling the power profile of the base design, P_(nominal), according tothe following equations to obtain the power profile at the prescribedprescription, Rx, or degree of ametropia,P ₂(r)=P _(nominal)(r)+SA _(eye) *r ² +Rx−Rx _(nominal), andP _(Rx)(r)=P ₂(M*r)−SA _(eye) *r ², wherein SA_(eye) is the sphericalaberration and r is the radial distance from the center of the lens. 12.The method for improving ophthalmic lenses for the treatment ofpresbyopia according to claim 7, wherein the step of scaling the radiallocation of the predetermined features within the base optical design inproportion to a measure pupil size of an individual comprises:determining magnification factors M₁ through M_(n) that relates thepupil sizes at a range of luminance levels for the ametropia level ofthe base design to the measured pupil size for the same luminance of theindividual; and scaling the power profile of the base design, P nominal,according to the following equations to obtain the power profile at theprescribed prescription, Rx, or degree of ametropia,P ₂(r)=P _(nominal)(r)+SA _(eye) *r ² +Rx−Rx _(nominal), andP _(Rx)(r)=P ₂(M ₁ *r+M ₂ *r ²+ . . . )−SA _(eye) *r ₂, wherein SA_(eye)is the spherical aberration and r is the radial distance from the centerof the lens.
 13. A method for improving ophthalmic lenses for thetreatment of presbyopia, the method comprising the steps of: creating abase optical design with predetermined features for a lens for treatingpresbyopia; determining the power profile of the base optical design ata nominal prescription power; creating a visual merit function foroptimization; and minimizing the difference between the visual meritfunction at the nominal prescription power and the visual merit functionat the prescription powers other than at the nominal prescription power.14. The method for improving ophthalmic lenses for the treatment ofpresbyopia according to claim 13, wherein the step of creating a visualmerit function for optimization comprises: determining the throughvergence visual metric for low, medium, and high luminance levels forthe base optical design; and calculating the difference between thethrough vergence for the base optical design and the through vergencefor the target degree of ametropia based using population average pupilsizes at low, medium and high luminance values.
 15. The method forimproving ophthalmic lenses for the treatment of presbyopia according toclaim 13, wherein the step of creating a visual merit function foroptimization comprises: determining the through vergence visual metricfor low, medium, and high luminance levels for the base optical design;and calculating the difference between the through vergence for the baseoptical design and the through vergence using the measured pupil sizesof an individual at low, medium and high luminance values.
 16. A set oflenses for treating presbyopia over a range of degrees of ametropia, theset of lenses being designed by creating a base optical design withpredetermined features for a lens for treating presbyopia, determiningthe power profile of the base optical design, P_(nominal), and scalingthe radial location of the predetermined features within the baseoptical design in proportion to the population average pupil size forthe degree of ametropia of a target individual.
 17. The set of lensesfor treating presbyopia over a range of degrees of ametropia accordingto claim 16, wherein the set of lenses comprises contact lenses.
 18. Theset of lenses for treating presbyopia over a range of degrees ofametropia according to claim 16, wherein the set of lenses comprisesintraocular lenses.
 19. A set of lenses for treating presbyopia over arange of degrees of ametropia, the set of lenses being designed bycreating a base optical design with predetermined features for a lensfor treating presbyopia, determining the power profile of the baseoptical design, P_(nominal), and scaling the radial location of thepredetermined features within the base optical design in proportion to ameasured pupil size of an individual.
 20. The set of lenses for treatingpresbyopia over a range of degrees of ametropia according to claim 19,wherein the set of lenses comprises contact lenses.
 21. The set oflenses for treating presbyopia over a range of degrees of ametropiaaccording to claim 19, wherein the set of lenses comprises intraocularlenses.
 22. A set of lenses for treating presbyopia over a range ofdegrees of ametropia, the set of lenses being designed by creating abase optical design with predetermined features for a lens for treatingpresbyopia, determining the power profile of the base optical design ata nominal prescription power, creating a visual merit function foroptimization, and minimizing the difference between the visual meritfunction at the nominal prescription power and the visual merit functionat the prescription powers other than at the nominal prescription power.23. The set of lenses for treating presbyopia over a range of degrees ofametropia according to claim 22, wherein the set of lenses comprisescontact lenses.
 24. The set of lenses for treating presbyopia over arange of degrees of ametropia according to claim 22, wherein the set oflenses comprises intraocular lenses.
 25. A set of lenses for treatingpresbyopia over a range of degrees of ametropia, the set of lenses beingdesigned with a power profile given byP _(Rx)(r)=P ₂(M ₁ *r+M ₂ *r ²+ . . . )−SA _(eye) *r ²,where P₂ is given byP ₂(r)=P ₁(r)+Rx,andP1(r)=P _(nominal)(r)−Rx _(nominal) +SA _(eye) *r ², where SA_(eye) isthe spherical aberration, r is the radial distance from the center ofthe lens, and P_(nominal)(r) is the power profile for the nominal designfor the correction of an eye with a spherical refractive need ofRx_(nominal) diopters.